Finite Group Databasebeta

← C2×#21456042 #30548286

Subgroups — C2×#21456042 #30548286

Order 15616.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840239C211yesmaximal, characteristic, complemented
2#21456042C2116yesmaximal, direct product factor
3C2×#16840100C211yesmaximal, characteristic, complemented
4C2×#16840083C211yesmaximal, characteristic
5C2×#16840054C211yesmaximal, characteristic, complemented
6C2×#16840044C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839917C211yesmaximal, characteristic, complemented
10C2×#16839900C211yesmaximal, characteristic
11C2×#16839867C211yesmaximal, characteristic, complemented
12C2×#16839862C211yesmaximal, characteristic, complemented
13C2×C4×#11758202C211yesmaximal, characteristic, complemented
14C2×C4×#11758200C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#542C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22#16840239—24no—
23#16840239C2218yescomplemented
24C2×C4×Dic122C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×#14519742—21no—
29C2×#14519742—21no—
30C2×#14519736C2211yescharacteristic
31C2×#14519733—21no—
32C2×#14519733—21no—
33#16840100C2218yescomplemented
34#16840083C2218yes—
35#16840054C2218yescomplemented
36#16840044C2218yescomplemented
37#16839981C2218yescomplemented
38#16839981C2218yescomplemented
39#16839917C2218yescomplemented
40#16839900C2218yes—
41#16839867C2218yescomplemented
42#16839862C2218yescomplemented
43C4×#11758202C2218yescomplemented
44C4×#11758200C2218yescomplemented
45#16839823C2218yescomplemented
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519700C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#542—24no—
65C61×#542C2218yes—
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—22no—
79C22×Dic122—24no—
80C22×Dic122—24no—
81C22×Dic122C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C23×Dic61—21no—
85C2×#11758202—24no—
86C2×#11758202—24no—
87C2×#11758202C2314yes—
88C2×#11758202C2314yes—
89C2×#11758200—24no—
90C2×#11758200—24no—
91C2×#11758200C2314yes—
92C2×#11758200C2314yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C4×Dic122—22no—
98C4×Dic122—22no—
99C4×Dic122—22no—
100C4×Dic122—22no—
101C4×Dic122C2314yes—
102C4×Dic122C2314yes—
103C4×Dic122C2314yes—
104C4×Dic122C2314yes—
105#14519742—28no—
106#14519742—28no—
107#14519736—22no—
108#14519736C2314yes—
109#14519733—28no—
110#14519733—28no—
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×C22⋊Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123#14519710C2314yes—
124#14519710C2314yes—
125#14519708C2314yes—
126#14519708C2314yes—
127C4⋊#92418C2314yes—
128C4⋊#92418C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519700C2314yes—
132#14519700C2314yes—
133#14519700C2314yes—
134#14519700C2314yes—
135#14519698C2314yes—
136#14519698C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yes—
139#14519688C2314yes—
140C4×#92418C2314yes—
141C22×Q8×C61—21no—
142C22×Q8×C61C2311yescharacteristic
143C22×D4×C61—21no—
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147C4⋊Q8×C61—22no—
148C4⋊Q8×C61C2314yes—
149#126×C61—28no—
150#124×C61—28no—
151#124×C61—22no—
152#124×C61C2314yes—
153#123×C61—28no—
154C22⋊Q8×C61—22no—
155C22⋊Q8×C61—28no—
156C22⋊Q8×C61C2314yes—
157#121×C61—22no—
158#121×C61C2314yes—
159C4×Q8×C61—22no—
160C4×Q8×C61C2314yes—
161C4×D4×C61—22no—
162C4×D4×C61C2314yes—
163#117×C61D414yes—
164#117×C61C2314yes—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—24no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—82no—
189C2×Q8×C61C2412yes—
190C2×D4×C61—24no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—82no—
195C2×D4×C61C2412yes—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—24no—
202C22×C4×C61—82no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2412yes—
210C22×C4×C61C2411yescharacteristic
211C22×Dic61—28no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C2×Dic122—28no—
218C2×Dic122—216no—
219C2×Dic122—24no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—28no—
225C2×Dic122—28no—
226C2×Dic122#4114yes—
227C2×Dic122#4114yes—
228C2×Dic122C2412yes—
229C2×Dic122C2412yes—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2×D414yes—
236C4⋊C4×C61C2×D414yes—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61C2×D414yes—
245C22⋊C4×C61C2×D414yes—
246C42×C61—24no—
247C42×C61C2×D412yes—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C42×C61C2412yes—
251C22⋊Dic61—24no—
252#11758202—28no—
253#11758202—28no—
254#11758200—28no—
255#11758200—28no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D412yes—
285C23×C61C22×D411yescharacteristic
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—42no—
289Q8×C61—84no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—42no—
293D4×C61—84no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—24no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—84no—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4112yes—
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2511yescharacteristic
318C2×Dic61—216no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327Dic122—216no—
328Dic122—24no—
329Dic122—24no—
330Dic122—22no—
331Dic122—22no—
332Dic122C2×#4114yes—
333Dic122C2×#4114yes—
334#92418—22no—
335#92418—22no—
336#92418—22no—
337#92418—22no—
338C2×#3121—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—44no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—84no—
347C22×C61#52512yes—
348C22×C61#57712yes—
349C22×C61#57812yes—
350C22×C61C23×D411yescharacteristic
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61#52512yes—
360C4×C61C22×#4111yescharacteristic
361C4×C61C22×#4111yescharacteristic
362Dic61—24no—
363Dic61—24no—
364Dic61—42no—
365Dic61—42no—
366C2×#542D6111yescharacteristic
367C2×#519—611no—
368#3121—6116no—
369C2×#485—611no—
370C2×#482—611no—
371C2×#477—611no—
372C2×#475—611no—
373C2×#464—611no—
374C2×#464—611no—
375C2×#451—611no—
376C2×#448—611no—
377C2×#441—611no—
378C2×#440—611no—
379C2×C4×Q16—611no—
380C2×C4×SD16—611no—
381C2×#433—611no—
382C2×C61—42no—
383C2×C61—82no—
384C2×C61#312114yescomplemented
385C2×C61C2×#52511yescharacteristic
386C2×C61C2×#57711yescharacteristic
387C2×C61C2×#57811yescharacteristic
388C23×Q8—611no—
389C22×Q16—611no—
390C22×Q16—611no—
391C22×SD16—611no—
392C22×SD16—611no—
393#542—24no—
394#542C2×D6118yes—
395C2×C4⋊Q8C2×D6111yescharacteristic
396C2×#126—21no—
397C2×#124—21no—
398C2×#124C2×D6111yescharacteristic
399C2×#123—21no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×#121C2×D6111yescharacteristic
403#519—618no—
404#519—1224no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—1221no—
410C2×C4×Q8—1221no—
411C2×C4×Q8C2×D6111yescharacteristic
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414C2×#117—1221no—
415C2×#117—1221no—
416C2×#117C2×D6111yescharacteristic
417#485—618no—
418#482—618no—
419#477—618no—
420#475—618no—
421#464—618no—
422#464—618no—
423#451—618no—
424#448—618no—
425#441—618no—
426#440—618no—
427C4×Q16—618no—
428C4×SD16—618no—
429#433—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×#97—611no—
447C2×C4×C8—611no—
448C61C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8—611no—
451C22×Q8—611no—
452C22×Q8—614no—
453C22×Q8—1224no—
454C22×Q8—1224no—
455C22×Q8—1221no—
456C22×Q8—1222no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C2×Q16—614no—
464C2×Q16—614no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×SD16—614no—
468C2×SD16—614no—
469C2×SD16—1224no—
470C2×SD16—1224no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D6114yes—
477#126—28no—
478#124—28no—
479#124—22no—
480#124C22×D6114yes—
481#123—28no—
482C22⋊Q8—22no—
483C22⋊Q8—28no—
484C22⋊Q8C22×D6114yes—
485#121—22no—
486#121C22×D6114yes—
487C4×Q8—22no—
488C4×Q8—614no—
489C4×Q8—614no—
490C4×Q8—614no—
491C4×Q8—614no—
492C4×Q8—1228no—
493C4×Q8—1228no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1222no—
498C4×Q8C22×D6114yes—
499C4×D4—22no—
500C4×D4C22×D6114yes—
501#117—614no—
502#117—1222no—
503#117—1228no—
504#117—1228no—
505#117C22⋊D6114yes—
506#117C22×D6114yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4C22⋊D6111yescharacteristic
517C2×C4⋊C4C22⋊D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4C22⋊D6111yescharacteristic
527C2×C22⋊C4C22⋊D6111yescharacteristic
528C2×C42—21no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42C22×D6111yescharacteristic
535C2×C42C22×D6111yescharacteristic
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540C4⋊C8—614no—
541C4⋊C8—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550C22⋊C8—614no—
551C22⋊C8—614no—
552#97—614no—
553C4×C8—614no—
554C24—21no—
555C24C2×C22⋊D6111yescharacteristic
556C2×Q8—21no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—82no—
561C2×Q8—614no—
562C2×Q8—614no—
563C2×Q8—612no—
564C2×Q8—612no—
565C2×Q8—1228no—
566C2×Q8—1228no—
567C2×Q8—1228no—
568C2×Q8—12216no—
569C2×Q8—1224no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8C23×D6112yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4C23×D6112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—1228no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4C2×C22⋊D6112yes—
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602Q16—1228no—
603Q16—1228no—
604SD16—1228no—
605SD16—1228no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C2×C8—1222no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—612no—
620C4⋊C4—612no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4C2×C22⋊D6114yes—
628C4⋊C4C2×C22⋊D6114yes—
629C4⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—1224no—
637C22⋊C4C2×C22⋊D6114yes—
638C22⋊C4C2×C22⋊D6114yes—
639C42—24no—
640C42—1224no—
641C42—1224no—
642C42—1224no—
643C42—1224no—
644C42—1224no—
645C42C2×C22⋊D6112yes—
646C42C2×C22⋊D6112yes—
647C42C23×D6112yes—
648C42C23×D6112yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D6112yes—
657C23C22×C22⋊D6111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—84no—
662Q8—614no—
663Q8—614no—
664Q8—12216no—
665Q8—1224no—
666Q8—1224no—
667Q8—1222no—
668Q8—1222no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—12216no—
689C2×C4—1224no—
690C2×C4—1224no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22×C22⋊D6112yes—
698C2×C4C22×C22⋊D6112yes—
699C2×C4C22×C22⋊D6112yes—
700C2×C4C22×C22⋊D6112yes—
701C2×C4C22×C22⋊D6112yes—
702C2×C4C22×C22⋊D6111yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4#41×D6112yes—
705C2×C4C24×D6111yescharacteristic
706C8—1222no—
707C8—1222no—
708C8—1222no—
709C8—1222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1684026912yes—
719C22#1684057312yes—
720C22#1684057712yes—
721C22C23×C22⋊D6111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—1224no—
731C4—1224no—
732C4—2442no—
733C4—2442no—
734C4#1684026912yes—
735C4C2×#41×D6111yescharacteristic
736C4C2×#41×D6111yescharacteristic
737C2—42no—
738C2—82no—
739C2#2145604214yesdirect product factor
740C2C2×#1684026911yescharacteristic
741C2C2×#1684057311yescharacteristic
742C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#542D61
hypocenterC61C2×#3121
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840239C2semidirect
2. #21456042C2direct (N × H)
3. C2×#16840100C2semidirect
5. C2×#16840054C2semidirect
6. C2×#16840044C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839917C2semidirect
11. C2×#16839867C2semidirect
12. C2×#16839862C2semidirect
13. C2×C4×#11758202C2semidirect
14. C2×C4×#11758200C2semidirect
15. C2×#16839823C2semidirect
23. #16840239C22semidirect
33. #16840100C22semidirect
35. #16840054C22semidirect
36. #16840044C22semidirect
37. #16839981C22semidirect
38. #16839981C22semidirect
39. #16839917C22semidirect
41. #16839867C22semidirect
42. #16839862C22semidirect
43. C4×#11758202C22semidirect
44. C4×#11758200C22semidirect
45. #16839823C22semidirect
384. C2×C61#3121semidirect
448. C61C2×#3121semidirect
739. C2#21456042direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168402392
#214560422
C2×#168401002
C2×#168400832
C2×#168400542
C2×#168400442
C2×#168399812
C2×#168399172
C2×#168399002
C2×#168398672
C2×#168398622
C2×C4×#117582022
C2×C4×#117582002
C2×#168398232
C2×C61×#5422
C2×#312161